Matrix Acidizing Design

Module 2 — Sandstone Acidizing: HF/HCl Three-Stage Design

def hf_hcl_stage_volumes(h_ft, r_w_ft, phi,
                           damage_radius_ft=2.0,
                           preflush_pv=0.5,
                           main_flush_pv=1.0,
                           overflush_pv=0.5):
    """
    Standard three-stage HF/HCl sandstone acid treatment design.
    Based on McLeod (1984) SPE 13798 guidelines.

    Stage 1 — Pre-flush: 5-7.5% HCl to dissolve CaCO3 and establish injection path
    Stage 2 — Main flush: 12% HCl + 3% HF (mud acid) to dissolve clays and fines
    Stage 3 — Overflush: NH4Cl or KCl brine to displace spent acid past perforations

    Volumes based on pore volumes in the damage zone (r_w to r_damage).

    Returns: stage volumes (gallons)
    """
    # Pore volume of damage zone per ft of perforated interval
    pv_damage_ft3 = math.pi * (damage_radius_ft**2 - r_w_ft**2) * phi * h_ft
    pv_damage_gal = pv_damage_ft3 * 7.48052

    # Stage volumes as multiples of damage zone pore volume
    preflush_gal = preflush_pv * pv_damage_gal
    main_flush_gal = main_flush_pv * pv_damage_gal
    overflush_gal = overflush_pv * pv_damage_gal
    total_gal = preflush_gal + main_flush_gal + overflush_gal

    return {
        "preflush_gal": round(preflush_gal, 0),
        "preflush_bbl": round(preflush_gal / 42.0, 1),
        "main_flush_gal": round(main_flush_gal, 0),
        "main_flush_bbl": round(main_flush_gal / 42.0, 1),
        "overflush_gal": round(overflush_gal, 0),
        "overflush_bbl": round(overflush_gal / 42.0, 1),
        "total_gal": round(total_gal, 0),
        "total_bbl": round(total_gal / 42.0, 1),
        "stage1_system": "5-7.5% HCl pre-flush",
        "stage2_system": "12% HCl + 3% HF (mud acid)",
        "stage3_system": "2% KCl brine overflush"
    }

def hf_acid_system_selection(clay_content_frac, carbonate_content_frac,
                               temperature_f):
    """
    Recommend HF acid system based on mineralogy.
    Based on SPE 13798 (McLeod 1984) and Schechter acid selection table.
    Returns: recommended acid system and rationale.
    """
    if carbonate_content_frac > 0.10:
        note = "Pre-flush volume should be increased; high carbonate will consume HF rapidly"
    else:
        note = "Standard HCl:HF ratios acceptable"

    if temperature_f > 200:
        system = "Organic HF (acetic acid + HF) or retarded HF — high T increases reaction rate"
    elif clay_content_frac > 0.15:
        system = "Low-concentration mud acid (6% HCl + 1.5% HF) or sequential HF — high clay content"
    elif clay_content_frac < 0.05:
        system = "Standard mud acid (12% HCl + 3% HF) — low clay, clean sandstone"
    else:
        system = "Standard mud acid (12% HCl + 3% HF) — moderate clay content"

    return {"recommended_system": system, "note": note,
            "temperature_f": temperature_f,
            "clay_content_pct": round(clay_content_frac * 100, 1)}

Module 3 — Post-Acid Skin: Hawkins Formula

def hawkins_skin(k_formation_md, k_altered_md,
                  r_altered_ft, r_w_ft):
    """
    Hawkins formula for composite skin factor.
    S = (k_f/k_a - 1) * ln(r_a / r_w)

    k_formation: formation permeability beyond damage/alteration zone (md)
    k_altered:   permeability of the altered (acid-treated) zone (md)
    r_altered:   radius of the altered zone (ft)
    r_w:         wellbore radius (ft)

    For a DAMAGED zone: k_altered < k_formation  => S > 0 (damage)
    For an ACIDIZED zone: k_altered > k_formation => S < 0 (stimulation)
    Returns: skin factor (dimensionless)
    """
    if k_altered_md <= 0 or r_altered_ft <= r_w_ft:
        return None
    return (k_formation_md / k_altered_md - 1.0) * math.log(r_altered_ft / r_w_ft)

def skin_bypass_effective_rw(S_post_acid, r_w_ft):
    """
    Effective wellbore radius after stimulation:
    r_wa = r_w * exp(-S)
    Negative skin (stimulated) gives r_wa > r_w, equivalent to a larger wellbore.
    """
    return r_w_ft * math.exp(-S_post_acid)

def production_ratio_after_acid(S_before, S_after, r_e_ft, r_w_ft):
    """
    Production ratio (stimulation ratio) from skin improvement.
    q_after/q_before = (ln(re/rw) - 0.75 + S_before) / (ln(re/rw) - 0.75 + S_after)
    """
    ln_ratio = math.log(r_e_ft / r_w_ft) - 0.75
    return (ln_ratio + S_before) / (ln_ratio + S_after)

def post_acid_damage_composite(r_w_ft, r_acid_ft, r_damage_ft,
                                 k_undamaged_md, k_acid_md, k_damage_md):
    """
    Total skin for three-zone composite: undamaged + damaged + acid-treated.
    S_total = S_damage + S_acid
    where S_damage uses original damage zone and S_acid uses acid alteration.
    Useful for partial acid penetration scenarios.
    """
    S_damage = hawkins_skin(k_undamaged_md, k_damage_md, r_damage_ft, r_w_ft)
    S_acid = hawkins_skin(k_undamaged_md, k_acid_md, r_acid_ft, r_w_ft)
    # Acid penetrates the damage zone: composite = S_acid (acid zone replaces damage)
    # if r_acid >= r_damage: S_total = S_acid (damage fully bypassed)
    if r_acid_ft >= r_damage_ft:
        S_total = hawkins_skin(k_undamaged_md, k_acid_md, r_acid_ft, r_w_ft)
    else:
        # Partial penetration: acid zone inside damage zone
        S_inner = hawkins_skin(k_damage_md, k_acid_md, r_acid_ft, r_w_ft)
        S_outer = hawkins_skin(k_undamaged_md, k_damage_md, r_damage_ft, r_w_ft)
        S_total = S_inner + S_outer
    return {"S_total": round(S_total, 2),
            "S_undamaged_skin_original": round(S_damage, 2),
            "S_after_acid": round(S_acid if r_acid_ft >= r_damage_ft else S_total, 2)}

Module 4 — Maximum Injection Rate Below Fracture Pressure

def max_matrix_injection_rate(k_md, h_ft, P_frac_psia, P_res_psia,
                                mu_acid_cp=1.0, B=1.0,
                                r_e_ft=1000.0, r_w_ft=0.33, S=0.0):
    """
    Maximum injection rate to stay below fracture pressure (Darcy radial flow).
    q_max = k*h*(P_frac - P_res) / [141.2*B*mu*(ln(re/rw) - 0.75 + S)]
    Use 90% of q_max as operating target for safety margin.
    Returns: q_max (bbl/day), q_max_bpm (bbl/min)
    """
    if k_md <= 0 or h_ft <= 0:
        return None
    ln_term = math.log(r_e_ft / r_w_ft) - 0.75 + S
    q_max_bpd = k_md * h_ft * (P_frac_psia - P_res_psia) / (141.2 * B * mu_acid_cp * ln_term)
    return {
        "q_max_bpd": round(q_max_bpd, 1),
        "q_max_bpm": round(q_max_bpd / 1440.0, 4),
        "q_target_bpm": round(0.90 * q_max_bpd / 1440.0, 4),
        "note": "Target 90% of q_max; stop if ISIP exceeds frac gradient"
    }

def frac_gradient_psi_ft(overburden_gradient=1.0, biot_coeff=0.7,
                           poisson_ratio=0.25, pore_pressure_gradient=0.465):
    """
    Minimum horizontal stress / fracture gradient estimate.
    sigma_h_min = nu/(1-nu) * (S_v - alpha*P_p) + alpha*P_p
    Expressed as gradient (psi/ft TVD).
    Use as conservative estimate — actual FG from leak-off test (LOT) preferred.
    """
    sigma_v = overburden_gradient
    alpha = biot_coeff
    nu = poisson_ratio
    P_p = pore_pressure_gradient
    sigma_h = nu / (1.0 - nu) * (sigma_v - alpha * P_p) + alpha * P_p
    return round(sigma_h, 3)  # psi/ft

Learning Resources

Textbooks

Key SPE References

Free Online Resources

WVU Courses

• PNGE 341 Well Completions and Stimulation — primary course for acidizing
• PNGE 361 Production Engineering — post-acid skin and PI improvement context

Output Format

## Matrix Acid Treatment Design — [Well / Formation]

### Formation Characterization
| Parameter | Value | Source |
|-----------|-------|--------|
| Formation type | Carbonate / Sandstone | |
| Permeability (k) | md | Core/test |
| Porosity (phi) | fraction | Log |
| Damage radius | ft | Estimated |
| Skin before treatment | dimensionless | Well test |
| Temperature | degF | BHT |

### Treatment Design (Carbonate)
| Stage | Fluid | Concentration | Volume (bbl) | Rate (bpm) |
|-------|-------|---------------|-------------|-----------|
| Pre-flush | HCl | 15% | | |
| Main flush | HCl | 15–28% | | |
| Overflush | KCl brine | 2% | | |

OR (Sandstone):
| Stage | Fluid | System | Volume (bbl) | Rate (bpm) |
|-------|-------|--------|-------------|-----------|
| Pre-flush | HCl | 7.5% HCl | | |
| Main flush | Mud acid | 12/3 HCl/HF | | |
| Overflush | NH4Cl | 2% | | |

### Expected Results
| Metric | Before | After |
|--------|--------|-------|
| Skin factor | | |
| Effective r_wa (ft) | | |
| Production ratio | 1.0 | |

**Certainty:** MEDIUM (design) | LOW (expected skin; actual depends on formation response)
**Bias:** Volumes are minima; field execution should monitor ISIP and adjust in real time

Error Handling

Caveats

• Fracture initiation must be avoided. Confirm frac gradient from LOT/FIT before designing injection rates. Monitor ISIP in real time.
• Wormhole models are scale-dependent. Core-scale PVBT does not directly translate to field scale. Field wormhole efficiency is typically lower.
• HF incompatibility with crude oil can form iron sludge. Run compatibility tests before pumping HF in wells with paraffinic or asphaltic crude.
• Sandstone acid sequence is strict: HCl pre-flush must precede HF; pumping HF into a CaCO3-rich zone without HCl pre-flush generates CaF2 precipitation.
• For Marcellus/Utica: these are primarily hydraulic fracture completions, not matrix acid candidates. Matrix acidizing is more relevant for naturally fractured carbonates (Knox Dolomite, Onondaga) or near-wellbore damage removal in conventional completions.